Space walking is poorly named, as it has little in common with how animals walk on Earth. Space walking is more akin to mountain climbing in scuba gear, while parachuting in a freefall -- an odd combination of effects and equipment to help people do a demanding job. Robots are now being studied for service in this same domain, working on large scale space structures like the Space Station, servicing science or military platforms in high orbit, or riding on the outside of a space craft in transit to Mars, the Moon or other destinations. What have we learned about climbing in 0g? How should machines be controlled for serving in this role? What can they do to overcome the problems that humans have faced? In order to move about in this environment, a robot must be able to climb autonomously, using gaits that smoothly manage its momentum and that minimize contact forces (walking lightly) while providing for safety in the event of an emergency requiring the system to stop. All three of these objectives are now being explored at NASA's Johnson Space Center, using the Robonaut system and a set of mockups that emulate the 0g condition. NASA's goal for Robonaut is to develop the control technology that will allow it to climb on the outside of the Space Shuttle, the Space Station, and satellite mockups at JSC, enabling the robot to perform EVA task setups or serve as an Astronaut's assistant.